# Properties

 Label 320.2.c Level $320$ Weight $2$ Character orbit 320.c Rep. character $\chi_{320}(129,\cdot)$ Character field $\Q$ Dimension $10$ Newform subspaces $4$ Sturm bound $96$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$320 = 2^{6} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 320.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$96$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$3$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(320, [\chi])$$.

Total New Old
Modular forms 60 14 46
Cusp forms 36 10 26
Eisenstein series 24 4 20

## Trace form

 $$10q + 2q^{5} - 10q^{9} + O(q^{10})$$ $$10q + 2q^{5} - 10q^{9} - 8q^{21} + 2q^{25} + 4q^{29} - 12q^{41} + 30q^{45} - 2q^{49} + 20q^{61} + 16q^{65} - 72q^{69} + 18q^{81} - 32q^{85} - 28q^{89} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(320, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
320.2.c.a $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1+i)q^{5}+3q^{9}+2iq^{13}+4iq^{17}+\cdots$$
320.2.c.b $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{3}+(1+i)q^{5}+iq^{7}-q^{9}-4q^{11}+\cdots$$
320.2.c.c $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{3}+(1-i)q^{5}+iq^{7}-q^{9}+4q^{11}+\cdots$$
320.2.c.d $$4$$ $$2.555$$ $$\Q(i, \sqrt{5})$$ $$\Q(\sqrt{-5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{3}q^{7}+(-3+2\beta _{2}+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(320, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(320, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(160, [\chi])$$$$^{\oplus 2}$$